Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Tumble mills are hollow cylindrical shells of large diameter carrying grinding media (a combination of rock/iron ore/chemical flakes and metal balls/rods), which, upon rotation of the mill, will be ground into fine powder. These mills rotate at low speeds using a gear reduction unit and often have vibration problems. These vibration problems result in increased gear wear and occasional catastrophic failures resulting in production loss. The objective of this research is to investigate the effect of oscillation of grinding media on torsional vibrations of the mill. A theoretical model was developed to determine the oscillating frequency of the grinding media. A 12" (0.3 m) diameter tumble mill test rig was built with a 0.5 hp DC motor. The rig is tested with sand and iron bb balls to simulate the industry process application. At low volume levels the grinding media oscillates like a rigid body as compared to higher volumes. It is shown that tumbling action of grinding media causes torsional excitation and hence its effect has to be considered in torsional vibration analysis. At starting, the load on the gears is much higher due to this oscillation.

This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.

Torsional vibration can be characterized as the cyclic variation of shaft speed, which can cause various failures in rotating machines, such as: gear-tooth breakage, blade-off due to blade fatigue in steam turbines, break-off of shafts, and overloading of components fitted onto the shaft. Commercially, there are only a few systems available that measure this type of vibration as compared to lateral vibration measurement systems. Most of these systems required modifications to the rotating machine, which in some cases are unacceptable. Therefore, it has become common practice to develop in-house torsional vibration measurement systems. A common measurement technique, called Time Interval Measurement (TIMS), calculates the instantaneous speed of the shaft from a frequency modulated carrier wave. Since torsional vibration is the cyclic variation of shaft speed, the shaft speed can be used to determine torsional vibration. Noise can be easily introduced into this type of system masking the torsional vibration; this was apparent in the measurement system developed by Kar, which was used as a baseline for the experiments conducted in this thesis. Various techniques were employed to reduce the effects of the noise in the measurement system, such as (1) created an algorithm, different than the one used by Kar, to calculate shaft speed, (2) increased the sampling rate of the data acquisition boards, (3) resampled the shaft speed into the order domain in order to remove harmonic noise, and (4) created an algorithm that corrects the shaft speed calculation to account for unequal spacing of encoder segments. These noise reducing techniques were compiled into a LabVIEW™ program in order to develop a robust measurement system. Each technique was tested individually on two test rigs constructed at the Turbomachinery Laboratory. Each technique proved to reduce the noise introduced into the system, but the geometric compensation algorithm proved to be the most effective in reducing the noise. This thesis proved that an in-house measurement system could be developed at a relatively low cost and with relative ease.

The objective of this study is the investigation of the mechanism responsible for the squeal vibrations excited when bodies with fairly rough surfaces are rubbed on a cold dry slightly compacted snow bed. To this end, signals were recorded and analyzed when the snow surface was rubbed by the ends of baseball bats, the ends of circular wood rods, and by the thick sole of a rubber boot. It is argued that the vibration modes are confined in the rubbing bodies and that the role of the snow bed is limited to providing the right conditions for the stick-slip effect to be applicable at the rubbing interface. An attempt is made to account for the reported very intense sound emission from a sheared very cold snow bed in terms of coherent snow granule column vibrations around the shearing body, as in the case of a sheared singing sand bed.

Whole-body vibration (WBV) has been shown to enhance vertical jump performance. The purpose of this study was to determine which WBV intensity has the greatest effect on counter movement jump (CMJ) height and the duration of that affect. Forty-four participants, of varying training statuses, were tested. They participated in > 4 familiarization sessions, to eliminate learning effects. Participants performed a pre-test, followed randomly by one of 5 WBV intensities. Participants performed 3 maximal CMJs immediately, 5, and 10 min following treatment. The best performance was used and calculated as a percentage of the pre-treatment values. A multivariate model (treatment X time X gender) was used to analyze the data. The three-way interaction approached significance (p=0.053) and significance was found for all two way interactions. Females performed the best immediately following the 2.71g treatment (116.9 + 38.4%). Male participants did not increase their performance; however, they may require longer durations of vibration exposure to elicit effects. The differences between males and females may also indicate that the effects of WBV are dependent on strength, stiffness, and/or training levels. Future research should continue to systematically investigate the effects of vibration and participant characteristics on WBV and performance.Keywords: power, frequency, amplitude, training, potentiation, stiffness. / School of Physical Education, Sport, and Exercise Science

Tuned vibration absorbers (TVAs) are spring-mass-damper devices used to mini-mize energy in a vibrating body. TVAs decrease in efficiency when the vibrating body is subjected to variable, broadband, or random excitation. A state-switched absorber (SSA) can be used in these variable, broadband, or random excitation cases to more effectively reduce excitation. An SSA is a mass-spring-damper where one or more of these elements can instantaneously and discretely change. An SSA was designed, built and tested to fit the specifications for TVAs found on ATR 72 and 42 airplane fuselages. A magnetorheological elastomer (MRE), an elastomer with imbedded iron particles, was selected as a variable spring. Flux lines concentrated through all MREs in absorber configurations. MREs containing 35% iron by volume yielded the largest frequency shift. A 35% MRE based absorber had a frequency range of 45-183 Hz, which corresponds to a 360% frequency increase. Transient absorber behavior was observed by recording rise and drop times to step field intensity changes.The 35% MRE absorber yielded a 0.20 second rise time and a 0.03 second drop time. Future work will determine whether a modified input signal can generate an appropriate transient response.

Torsional vibration can be characterized as the cyclic variation of shaft speed, which can cause various failures in rotating machines, such as: gear-tooth breakage, blade-off due to blade fatigue in steam turbines, break-off of shafts, and overloading of components fitted onto the shaft. Commercially, there are only a few systems available that measure this type of vibration as compared to lateral vibration measurement systems. Most of these systems required modifications to the rotating machine, which in some cases are unacceptable. Therefore, it has become common practice to develop in-house torsional vibration measurement systems. A common measurement technique, called Time Interval Measurement (TIMS), calculates the instantaneous speed of the shaft from a frequency modulated carrier wave. Since torsional vibration is the cyclic variation of shaft speed, the shaft speed can be used to determine torsional vibration. Noise can be easily introduced into this type of system masking the torsional vibration; this was apparent in the measurement system developed by Kar, which was used as a baseline for the experiments conducted in this thesis. Various techniques were employed to reduce the effects of the noise in the measurement system, such as (1) created an algorithm, different than the one used by Kar, to calculate shaft speed, (2) increased the sampling rate of the data acquisition boards, (3) resampled the shaft speed into the order domain in order to remove harmonic noise, and (4) created an algorithm that corrects the shaft speed calculation to account for unequal spacing of encoder segments. These noise reducing techniques were compiled into a LabVIEW™ program in order to develop a robust measurement system. Each technique was tested individually on two test rigs constructed at the Turbomachinery Laboratory. Each technique proved to reduce the noise introduced into the system, but the geometric compensation algorithm proved to be the most effective in reducing the noise. This thesis proved that an in-house measurement system could be developed at a relatively low cost and with relative ease.

Free vibration of beam with moderate thickness is analyzed in the present study. Plane strain finite element is employed, which is based on 2-D elasticity. The conventional displacement-type variational principle is combined with Reissner¡¦s principle and a mixed-type variational formulation is derived. With such formulation, stresses, as well as displacements, are the primacy variables and both boundary conditions can be imposed exactly and simultaneously. Beams with various aspect ratios and boundary conditions are analyzed. Vibration frequencies and modes are obtained and compared to those by Euler¡¦s beam theory, Timoshenko beam theory, higher-order theory and displacement-type plane strain finite element method to see the effects of 2-D elasticity beam analysis compared to traditional 1-D theories, and the satisfying of stress boundary conditions, in addition to the displacement ones.

This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.